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losalamos06talk1.ppt - Rice University

VIEWS: 1 PAGES: 45

									Relativistic Plasmas in Astrophysics
    and in Laser Experiments I:
PIC Simulations of Poynting Jets and
        Collisionless Shocks

        Edison Liang, Koichi Noguchi
               Rice University

Acknowledgements: Scott Wilks, Bruce Langdon
    (lecture series at LANL July, 2006)
    Work supported by LLNL, LANL, NASA, NSF
This talk will focus on particle
acceleration and radiation of:

1. Poynting jets = EM-dominated
     directed outflows

2. Relativistic collisionless shocks
High Energy                    Relativistic
Astrophysics                  Plasma Physics


                 Particle
               Acceleration


   New                        Ultra-Intense
Technologies                     Lasers
   Phase space of laser plasmas overlaps most of relevant
             high energy astrophysics regimes
         PulsarWind

                                 GRB
     4
                                          High-b
     3
                       Blazar
log<g>

     2

                   INTENSE LASERS
     1     Low-b
                            Galactic Black Holes
     0
               100     10        1       0.1       0.01
                              W /w
Pulsar equatorial striped wind from oblique rotator




                                (Lyubarsky 2005)




                               collisionless shock
   Gamma-Ray Bursts: Two Competing
  Paradigms: “to B(magnetic) or not to B?”




                             Woosley & MacFadyen,
                             A&A. Suppl. 138, 499 (1999)



               e+e-
                                                           e+e-
Internal shocks: What is primary energy source? Poynting flux:
Hydrodynamic How are the e+e- accelerated? Electro-magnetic
                 How do they radiate?           -dominated
Outflow
                                                Outflow
Relativistic Plasmas Cover Many Regimes:
  1. kT or internal <g> > mc2

  2. Flow speed vbulk ~ c (G >>1)

  3. Strong B field: vA/c = S1/2 = We/wp > 1

  4. Vector potential ao=eE/mcwo > 1

   Most of these regimes are “collisionless”
       They can be studied mainly via
     Particle-in-Cell (PIC) simulations
                 Side Note

          MHD, and in particular,
 magnetic flux freezing, often fails in the
 relativistic regime, despite small gyroradii.
This leads to many novel, counter-intuitive
       kinetic phenomena unique to the
             relativistic regime.
 Moreover, nonlinear collective processes
    behave very differently in the ultra-
   relativistic regime, due to v=c limit.
                Example of




      x

                          y (into
                          plane)




            in NN code. x is open   In dynamic problems, we ofte
in Zohar code.                      zones << initial Debye length
          What astrophysical scenarios may give rise
            to Poynting jet driven acceleration?
 Popular GRB Scenario            magnetic tower
                                 head w/ mostly
                                 toroidal field
                                 lines

                                                                   loc
                                                                  cylin


rising flux rope
from BH
accretion disk


                               collapsar               global torus
                               envelope           rapid deconfinement
                                     Particle acceleration by relativistic
           EM pulse
                                                  j x B force
 By        Entering
           Plasma
                JxB force snowplows all
                surface particles upstream:
Ez                                          y
                <g> ~ max(B2/4pnmec2, ao)
                “Leading Poynting                     By                   Ez
      Jz        Accelerator” (LPA)
           x

                                                                             Jz       JxB
               Exiting                                                            x
               Plasma                      z
                                                                              k
               JxB force pulls out surface particles. Loaded EM pulse (speed < c)
               stays in-phase with the fastest particles, but gets “lighter” as slower
               particles fall behind. It accelerates indefinitely over time:
               <g> >> B2 /4pnmec2, ao “Trailing Poynting Accelerator”(TPA).
           x   (Liang et al. PRL 90, 085001, 2003)
               t.We=800   t.We=10000
     TPA                               magnify
reproduces
many GRB
 signatures:
   profiles,
   spectra
and spectral
  Evolution
  (Liang &
 Nishimura
   PRL 91,
   175005
    2004)

We/wpe =10
Lo=120c/We
Details of early e+e- expansion




         Momentum gets more and
         more anisotropic with time
        ~0--1.5
                                   Epk
tWe=1000             Epk~200 keV
                                                     hard-to-soft
                                          dN/dt
  logdN/dE
                                                     GRB spectral
                   b~-2--2.5                         evolution

     5000     logE                       time




  10000
                                                        diverse
                                                        and
    18000                                               complex
                                                        BATSE
                                                        light
                                                        curves




                       Fourier peak wavelength scales as ~ c.gm/ wpe
       QuickTime™ an d a
    Anima tion d ecompressor
 are need ed to see this picture.




(movie by Noguchi 2004)
TPA produces Power-Law spectra with low-energy cut-off.
    Peak Lorentz factor gmcorresponds roughly to the
         profile/group velocity of the EM pulse
                                                Typical GRB spectrum
                                     ~0--1.5
      gm                                             Epk~200 keV


                              logdN/dE
                                                 b~-2--2.5
                                                b=(n+1)/2

                                             logE

      the maximum gmax ~ e E(t)bzdt /mc where E(t)
              is the comoving electric field
We/wep=10
                               We/wep=10
                               0




            f=1.33
            Co=27.9




gm(t) = (2fWe(t)t + Co)1/2         t ≥ Lo/c
This formula can be derived analytically from
           first principles
Lorentz equation for particles in an EM pulse with E(t ,t),
B(t, t) and profile velocity bw

d(gbx)/dt = - bzWe(t)h(t)
d(gbz)/dt = -(bw- bx)We(t)h(t)
d(gby)/dt = 0
dg/dt = -bw bzWe(t)h(t)

For comoving particles with bw~ bx we obtain:
bz = - o/g; by = yo /g; bx = (g2 -1- o2 - yo2)1/2/g
po ~ transverse jitter momentum due to Ez

Hence: dg2/dt = 2 po We(t)h(t)bx

As g1, bx ~ 1: d<g2>/dt ~ 2 po We(t)<h>
     Integrating we obtain: <g2>(t) = 2f W (t).t + g   2
 The power-law index seems remarkably robust
independent of initial plasma size or temperature
       and only weakly dependent on B

                              Lo=105rce


   f(g)                           Lo= 104rce


                                          -3.5




                          g
3D cylindrical geometry with toroidal fields




                  QuickTime™ and a
                     decompressor
            are need ed to see this picture.




          (movies by Noguchi)
      QuickTime™ and a
         decompressor
are need ed to see this picture.
      QuickTime™ and a
        decompressor
are neede d to see this picture.
      QuickTime™ and a
        decompressor
are neede d to see this picture.
3D donut geometry with pure toroidal fields




                  QuickTime™ and a
                    decompressor
            are neede d to see this picture.




              (movies by Noguchi)
      QuickTime™ and a
        decompressor
are neede d to see this picture.
      QuickTime™ and a
       QuickTime™ and a
        decompressor
         decompressor
are neede d to see this picture.
are neede d to see this picture.
      QuickTime™ and a
        decompressor
are neede d to see this picture.
     PIC simulation allows us to compute the
     radiation directly from the force terms

            Prad = 2e2(F|| 2+ g2F+2) /3c

           where F|| is force along v
         and F+ is force orthogonal to v

   TPA does NOT radiate synchrotron radiation.
     Instead Prad ~ We2pz2sin2 << Psyn ~We2g2
 where pz is momentum orthogonal to both B and
Poynting vector k, and  is angle between v and k.
TPA Prad asymptotes to ~ constant level at late times   .




 Lo=120c/We             po=10          Lo=105c/We
TPA of initially cold plasma results in much lower radiation




                           po=0.5
Asymptotic Prad scales with We/wpe between 2nd and 3rd power




  We/wpe=102                  103                104
   We have added radiation damping to PIC code using the
        Dirac-Lorentz Equation (see Noguchi 2004) to
calculate radiation output and particle motion self-consistently

                                               reWe/c=10-3




         Averaged Radiated Power by the highest energy electrons
Using ray-tracing Noguchi has computed intensity and polarization
                histories seen by detector at infinity




                                                      We/wpe=10




                                                      We/wpe=102
TPA e-ion run


 e




ion
                  e+e-
 In pure e-ion
   plasmas,
 TPA transfers
  EM energy
 mainly to ion
component due
   to charge
  separation

                 e-ion
TPA of e-ion plasma gives weaker electron radiation
In mixture of e-ion and e+e- plasma, TPA selectively
       accelerates only the e+e- component
   e                                   ion
                    100% e-ion:
                  ions get most of
                 energy via charge
                     separation


   e+e-                                ion
                10%e-ion, 90%e+e-
                  : ions do not get
                 accelerated, e+e-
                 gets most energy
                PIC simulations of Relativistic Collisionless Shocks




3D run of
e+e-
running into
cold clumpy
e+e- (Noguchi
et al 2005)
Interaction of e+e- Poynting jet with cold ambient e+e- shows broad
  (>> c/We, c/wpe) transition region with 3-phase “Poynting shock”
                                                  By*100
        px                                                   ejecta



                                                       ambient




                                 f(g)

              ejecta                       ambient
              spectral                     spectral
              evolution                    evolution

                          g                            g
Prad of “shocked” ambient electron is lower than ejecta electron




       ejecta e-                              shocked ambient e-
       Propagation of e+e- Poynting jet into cold e-ion plasma:
 acceleration stalls after “swept-up” mass > few times ejecta mass.
Poynting flux decays via mode conversion and particle acceleration
                     px/mc                      pi




    ejecta e+                     ambient e-         ambient ion
                      x
                                                         pi*10
                By




                             By*100
   Poynting shock in e-ion plasma is very complex with 5 phases
 and broad transition region(>> c/Wi, c/wpe). Swept-up electrons are
accelerated by ponderomotive force. Swept-up ions are accelerated by
                  charge separation electric fields.


                   100pxi
       100By                                      ejecta e-

Prad                        100Ex
                                    f(g)
                       -10pxe                                         ejecta
         -10pxej                                                        e+

                                              ambient
                                                  ion

                                                            ambient
                                                                 e-

                                                        g
Prad of shocked ambient electron is comparable to the e+e- case




        ejecta e-                       shocked ambient e-
Examples of collisionless shocks: e+e- running into B=0 e+e- cold plasma
    ejecta hi-B, hi-g        weak-B, moderate g        B=0, low g

           100By
                   ejecta


                                                 100By   100Ex              100By
             swept-up         100Ex       -px swept-up
                                                                        -pxswrpt-up




                   swept-up

                                      ejecta

                               swept-up
                                                                 swept-up
                           SUMMARY

1. Poynting jet (EM-dominated outflow) can be a highly efficient,
   robust comoving accelerator, leading to ultra-high Lorentz factors.
2. TPA reproduces many of the telltale signatures of GRBs.
3. In 3D, expanding toroidal fields mainly accelerates particles along
   axis, while expanding poloidal fields mainly accelerates particles
   radially.
4. Radiation power of TPA is higher than collisionless shocks. But in
   either case it is much lower than classical synchrotron radiation.
   This solves the “cooling problem” of synchrotron shocks.
5. Structure and radiation power of collisionless shocks is highly
   sensitive to EM field strength.
6. In hybrid e+e- and e-ion plasmas, TPA preferentially accelerates
   The e+e- component and leave the e-ion plasma behind.

								
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